Free magazine, negative heights, and statistical methods

There is a magazine that you should know about. It’s called
Significance (link). With that name, it's hardly surprising that it has statistical content. Mathematical equations are kept to a minimum, and typically set off in
boxes. I highly recommend it. The reason why I’m writing about it today is that for 2013, you can read
it for free via their iPhone or Android app (information here). The magazine is normally for
subscribers only, but this offer is sponsored by the International Year of Statistics in
2013.

Significance used to be published solely by the Royal
Statistical Society, but recently it’s a joint effort between them and the
American Statistical Association.

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In the most recent issue, there is an intriguing article on the distribution of heights of adults. Of course, we know it's a Bell Curve. That's what statistics teachers tell us anyway. These authors ask if the distribution is indeed normal, then where are the people with negative heights? I am one of those statistics teachers so I was happy enough to spend 10 minutes or so to indulge the authors in this flight of fancy. (The question has no practical value but it's interesting nevertheless in the context of modeling.)

I won't repeat the calculations from that article. The
general lesson is that statistical—in this case, probability—models are not
theorems, and they don’t usually work for every conceivable case. In fact, the
normal distribution model works exceedingly well for all but an inconceivably
small number of cases, so it is an exceedingly useful model for all but a few cases.

This leads me to one of my pet peeves. I often encounter criticism of
statistical models of the form “this model assumes X, and X is violated by this
counter-example, and thus the model is falsified.” In this example, someone might
say: this model assumes the existence of negative heights, which is both absurd
and obviously wrong, therefore the model is falsified. The bottom line
is every model contains assumptions that are not universal, and this example shows that such models can still be useful.